Freund-Rubin Superpotentials Revisited

Neil Lambert gave a seminar today on his paper from earlier this year entitled "Flux and Freund-Rubin Superpotentials in M-Theory", which is a continuation of work begun here. As usual my desire for an efficient arrival, i.e. get there at start time +/-delta where delta is minimized by my journey resulted in a small additive delta, and so I missed the very beginning. I'm not sure this is crucial as most of the material was unfamiliar to me.

Anyway Neil was asking 2 key questions as I got there, about the vacua in the landscape or haystack:

-Is the standard model there?
-How special or generic is it, if it is indeed there?

At this point NL emphasised that Douglas et al. who are working on the landscape simply aim to count the number of vacua there are and not the probability density of each vacuum existing (which may or may not be a delta function). NL summarised that "the counting statistics of the vacua is maths, the probability density is the physics." In the coffee break afterwards he pointed out the potential usefulness of the counting statistics, in that one may be able to find for some cases (i.e. specific vacua criteria) an absolute count that is less than one, in which case there is no such vacuum. This tells us about the probability density of the vacua and in such cases we learn some physics. It seems, at least in London, that the landscape is not as quite the rage here as it is in North America at the moment, so this elaboration was needed.

In the introduction NL stated that in the talk we would be concentrating on M-theory vacua M_4 x X, and that for N=1 Minkowski vacua X is the group G_2. He then told us that over twenty years ago Freund and Rubin introduced a class of M-theory (D=11 supergravity back then) "compactifications" with spacetimes AdS_4xX. To obtain N=1 supersymmetry in this case X is weak G_2. Weak G_2 was defined as a pair of conditions on the three-form \phi and its dual *\phi contsructed in the theory:

d\phi=4\lamdba *\phi, d*\phi=0

At a later point NL mentioned that while G_2 is restored under the condition \lambda=0, it is not true to think of weak G_2 being close to G_2 for small values of \lamda. In the paper it is pointed out that this is expected as \lambda can be made small by increasing the volume of the manifold, but this clearly doesn't change the properties of the manifold in a non-trivial way. NL said that his paper was essentially redoing the paper of Beasley and Witten but with weak G_2 rather than G_2.

The main body of the talk closely followed the layout of the paper, but without giving the detail of the calculations, and was a lively talk, however since so much of this was alien to me I don't feel comfortable trying to regurgitate it here. So I will just give three of NL's summary points:

1. the consistent construction of the the potential and superpotential of the Freund-Rubin compactications in the presence of topological fluxes.
2. that when the fluxes were turned on the F-R terms were driven to zero, resulting in a non-supersymmetric minimum
3. there are no supersymmetric vacua other than F-R or pure G_2

A major concern of NL's was that the Kaluza-Klein modes arising from the compactification are of the same order as the cosmological constant, and he was particularly interested in looking for ways to lift a decently small, positive cosmological constant from the theory using a "KKLT mechanism". For NL this means not fine-tuning the KK terms to get the desired cosmological constant but rather seeing if it was even a possibility. One scheme he considered involved the wrapping of a 9-cycle at which point he stopped and admitted, with spirit, that he didn't think there was a single person who beleived in a 9-brane. This was perhaps the second-most humerous comment of NL's upbeat seminar, the first being upon a specialisation to the bosonic case when he said "since I'm a supersymmetry guy, I never talk about fermions." Quite right too - in truth, I only wish that I could.

After one question, Nicolas announced the usual "coffee and cookies" in the coffee room, which was greeted by a very silent joy and gratitude.